You may try heat plot. And if you want to see data behavior only,  then Bubble plot is also good option. But I would strongly suggest for BUBBLE plot if you want to see output like contour plot. And Heat plot if you want to see output like surface plot.

Dear if you know matlab then you problem is easily solved. First you input the data into the workspace. After that goto the plot tab and you will see the most suitable plot according to you data. Its amazing. 

First you should gain some information about matlab. Then its very simple.

You can try scatter plot command in  Matlab

It would help to know a bit more about the context: both the data and the audience you're visualising this for. Are the weights confidence levels, for example? If so, using a stronger shade for points with higher weights will convey certainty. Can you give more details? 

Dear Dr. Byrne

Assume we have two dimension data with their weights. For instance I attached a two dimensional data by their weights in Matlab.rar that weights are member of interval [0,1]. And I used hint of Dr. Vatsa to using bubble plot  to show my meaning that attached by name Scatter.jpg.

I interest could we create a shape like contour to describe sample space or not?

You certainly could do but the question remains: is this a meaningful visualisation of the data? Are the individual datapoints discrete entities or are they samples from a continuous surface? If you're not representing a continuous distribution then I'd suggest sticking with what you have there! 

I believe all things are distributed but when we face this distribution points show a meaningful behavior accept them as a continuous one and display them with line instead of a lot of points. Therefore the first step is gaining outline behavior of points to understand is it meaningful behavior or not.

Are you have different idea?

Alternatively, you can also use different size of symbols for representing the weighted groups, particularly when you have few groups. This is an example:

contour doesn't need 3 matrix of 2D to make you plot

ex: if you have a matrix A(100,200), matlab can make the contour plot and automatically put abscissa from 1to 100 and ordinate from 1to 200, you need the other 2 matrix (or vectors) to precise the coordinate for example if you have X (100,200) and Y(100,200) matrix of longitude and longitude your new plot will be in function of longitude and latitude.

and to answer your question, the better way to represents your weighted data is to normalize.

It is simple: you need only to divide your matrix by the weight and do contour later, i prefère contourf. the interpretation in this case will be easy, if i beleive that your variable here A is space depended you can easy say where your variable is stronger or weaker.

you can try to plot it with heatmap, for example you can use R (open source software) and ggplot2 package

Check here: https://github.com/mbostock/d3/wiki/Gallery

You will find a lot of chart examples which will for sure fulfill your needs.

Regards